Question: Simplify the following expression: $t = \dfrac{z}{6} + \dfrac{4z}{3}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $6$ and $3$ $\lcm(6, 3) = 6$ $ t = \dfrac{1}{1} \cdot \dfrac{z}{6} + \dfrac{2}{2} \cdot \dfrac{4z}{3} $ $t = \dfrac{z}{6} + \dfrac{8z}{6}$ $t = \dfrac{z +8z}{6}$ $t = \dfrac{9z}{6}$ Simplify the expression by dividing the numerator and denominator by 3: $t = \dfrac{3z}{2}$